A project manager is in charge of 3 ongoing projects, A, B, and C. Due to recent reorganization, the project manager can assign additional employees to the 3 projects. Each employee who is assigned to a project can reduce the time to complete the project. The table below summarizes the data for the 3 projects. For instance, at most 5 employees may be assigned to project A. Each employee assigned to project A reduces the completion time by 3 days. (For example, if 3 employees are assigned to project A, its completion time is reduced by 9 days.) Total 11 employees are available. The project manager must maximize the least reduction among all 3 projects. For instance, if we can reduce the completion time of projects A, B, and C by 6, 8, and 9 days, respectively, the least reduction among all 3 projects is 6 days. Please formulate an LP model that helps the project manager assign the 11 employees. Projects Maximum Number of Employees Reduction of Completion Time (days / employee) A B 5 6 3 4 C 4 3

A project manager is in charge of 3 ongoing projects, A, B, and C. Due to recent reorganization, the project manager can assign additional employees to the 3 projects. Each employee who is assigned to a project can reduce the time to complete the project. The table below summarizes the data for the 3 projects. For instance, at most 5 employees may be assigned to project A. Each employee assigned to project A reduces the completion time by 3 days. (For example, if 3 employees are assigned to project A, its completion time is reduced by 9 days.) Total 11 employees are available. The project manager must maximize the least reduction among all 3 projects. For instance, if we can reduce the completion time of projects A, B, and C by 6, 8, and 9 days, respectively, the least reduction among all 3 projects is 6 days. Please formulate an LP model that helps the project manager assign the 11 employees. Projects Maximum Number of Employees Reduction of Completion Time (days / employee) A B 5 6 3 4 C 4 3

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

See similar textbooks

Similar questions

INTRODUCTION TO OPERATIONS RESEARCH
Modify the machine-to-job assignment model under the assumption that only three of the four jobs must be completed. In other words, one of the four jobs does not have to be assigned to any machine. What is the new optimal solution?
4. A large donor has come on board to support the city in this initiative. This donor has given the city $100,000 dollars for the program but has specified that the money MUST be used to promote the program to families. Therefore, management has decided that this money will be the project advertising budget. The goal of this advertising budget is to maximize the number of people reached. The ads must be ordered ahead of time and there are 3 different types of ads to choose from. There is Television, Billboards, and Social media. It is assumed that every ad purchased is used and the number of people reached is listed below. These ads are subject to the following constraints: A) Television ads require 2 hours of labor and cost $2k each B) Social Media ads require 1 hour of labor and cost $1k each C) Billboards require 5 hours of labor and cost $6K each MEDIA # OF PEOPLE REACHED PER AD Television 30K Social Media Billboards 25K 22K Formulate the advertising linear model and solve for the…
A manufacturing system is used to produce a product.Each unit of product must be processed sequentially through workstations.V -----> W -----> X -----> Y The processing time on each workstation are as follows:Workstation V, 11 minutes per unit,Workstation W, 6 minutes per unit,Workstation X, 19 minutes per unit,Workstation Y, 19 minutes per unit. The raw material is always available in the front of workstation V. The manufacturing system can produce __________ units in 27 hours. Use at least 4 decimals.You must show your calculation steps and brief explanation on your Excel spreadsheets.
Mangement Project management is the discipline of planning, organizing, motivating, and controlling resources to achieve specific goals and objectives within a specified time frame. It involves identifying project requirements, defining scope, establishing timelines, allocating resources, and managing risks. Project managers oversee the execution of projects, ensuring that they are completed on time, within budget, and according to quality standards. Effective project management requires strong leadership, communication, and problem-solving skills, as well as the ability to adapt to changing circumstances and stakeholders' needs. It is crucial for achieving project success and delivering value to stakeholders. Question: How does project management contribute to organizational efficiency and effectiveness?
A production line is to be designed for a job with four tasks. The task times are 2.4 minutes, 0.4 minutes, 0.9 minutes, and 2.7 minutes. After line balancing, the largest possible assigned cycle time is cycle time is 6.4; 2.7 minutes, and the smallest possible assigned minutes. O 2.7, 0.4 O 6.4, 2.4 O1.6, 0.4 18, 1.4
Amanufacturer is designing a product layout for a new product production. It plans to use a production line for 8 hours per day in order to meet forecasted demand of 180 units per day. The product requires 7 tasks in total. These tasks are namely,. A. B, C, D, E. F.and Grespectively, TaskAdoes not have any predecessor to start. To start Task B, it requires Task Ato be completed. Starting tasks Cneeds, the task B to be completed. Also, starting task D needed task B to be completed. Task E can only start upon completion of Task C. Whereas starting task Fneeds the completion of both the tasks Dand E. Finally, starting task Gneeded, task F to be completed. The processing times for tasks. A. B, C. D.E.F. and Gare 2.4, 22,0.9, 10, 1.2. 1.8, are 1.5 minutes respectively. Applying the most remaining tasks rule for balancing the assembly line, with ties broken according to longest task time first, the tasks that will be assigned to the THIRD workstation are O a D,E.and F Ob. D.E Oc CandE Od.…
There are four critical paths in a network. A-B-C-D-E, A-F-E, A-B-H-J-K-E and A-S-T-E. Each activity in this network can be crashed by a maximum of 6 weeks. The crashing cost (per week), for the first week (crashing first time), for activity A is: $480, E is $495 and all other activities is : $120 (per week per activity). The crashing cost, second week and onwards(crashing second time), for activity A is $1200 per week, E is $1440 per week and for all other activities is $240 per activity per week. You have a maximum crashing budget of $3005. The maximum possible reduction in the project duration will be: a. 6 weeks b. 3 weeks c. 2 week d. 5 weeks e. 4 weeks
Task 4In this task, you are asked to formulate the linear programming problem below andthen solve it.A carpenter produces Tables (T) and Chairs (C).Each Table unit requires 6kg of wood and 1kg of plastic.Each Chair unit requires 4kg of wood and 4kg of plastic.The carpenter has only 100kg of wood and only 50kg of plastic in stock.On each sale, the carpenter makes a profit of £15 per Table unit sold and a profit of£30 per Chair unit sold.Required:Formulate the Linear Programming problem above by defining the variables,stating the object function and the constraints.You are required to produce the graph for all inequalities (copy image to Word)Find the quantity to make of Tables and Chairs to maximise profit.
An office complex is to be renovated. Before the job can be completed, various tradespeople and skilled workers must install their materials. The table for this problem describes the relationships between the activities that need to be completed. Activity Immediate Predecessors Time (days) A1 - 6 A2 A1 7 A3 A1 3 A4 A1 10 A5 A2 10 A6 A3, A4 4 A7 A4 8 A8 A4 5 A9 A5, A6, A7 7 A10 A8 6 a) Develop a project network for this problem. b) Determine the EST, EFT, LST, LFT, and slack for each activity. c) What is the critical path and project completion time? d) Submit your file
Consider the AON graph of a project shown below. Figure 19.18 A1 to A2. A2 splits to A3 and A5. The path from A3 is A3, A4 A8 and A3, A6, A7, A8. The path from A5 is A5, A7, A8. The activity times are 3, 3, 1, 5, 5, 1, 2, and 2 days for activities A1 through A8, respectively. What is the earliest completion time of the project?
2. List down all the possible paths from vertex 'a' to vertex 'h'. Arrange your answer from the longest to the shortest path. If the paths have equal values, arrange them alphabetically in ascending order. Answer in this format: a-b-c-d-e-f, each vertex should only be used once in each path, closed-loops are not allowed. 3 (b) 3 2 2 3 4 2 f Longest Path 5 3 4 Shortest Path Note: Do not include the paths: a-d-g-f-c-e-h and a-d-g-f-c-b-e-h